Your "... used successfully" caveat disqualifies me from replying (since I'm now constructing my first ROV). But I'll reply anyway. I see several advantages to onboard batteries. First, you won't have the line losses and voltage drops of long-distance low-voltage transmission. Second, tether buoyancy problems are much reduced by having no heavy conductors. Third, onboard batteries provide useful ballast.
On the negative side, onboard batteries require a fairly sizable container that is both reliably sealed and easily accessible. Maybe not such an easy trick.
My initial idea for battery type was Li-Ion. But battery vendors have scared me off them. You actually have to pass a test before they'll sell them to you! They're just flat-out dangerous, especially in novice hands. Depending on what mistake you make, you get to choose whether your shop burns down or is blown-up.
My current choice is Nimh. There is a 1.2 volt "F"-size cell (1.3" dia. x 3.7" long). 10 of them makes 12 volts.
http://www.batteryspace.com has a lot of useful info on all types of batteries.
I invite comments on these ramblings. --Pilikia